Introduction to Fluid Mechanics (Winter Semester 2024/25)
- Lecturer: JProf. Dr. Xian Liao
- Classes: Lecture (0165900), Problem class (0165910)
- Weekly hours: 3+1
The motion of fluids is ubiquitous in our daily lives and can be described mathematically by two fundamental partial differential equations: the Euler equations and the Navier-Stokes equations. Although many intriguing open problems remain in the mathematical theory of solutions to these models, some well-established theories address fundamental problems concerning the existence and uniqueness of solutions. The mathematical analysis is highly sensitive to the types and parameters of the models; for example, the solutions of the Euler equations for inviscid fluids and those of the Navier-Stokes equations for viscous fluids exhibit notably different analytical properties.
| Schedule | ||
|---|---|---|
| Lecture: | Tuesday 14:00-15:30 | 20.30 0.19 |
| Problem class: | Friday 9:45-11:15 | 20.30 SR 2.66 |
| Lecturers | ||
|---|---|---|
| Problem classes | M. Sc. Rebekka Zimmermann | |
| Office hours: by appointment | ||
| Room 3.030 Kollegiengebäude Mathematik (20.30) | ||
| Email: rebekka.zimmermann@kit.edu | ||
Time plan:
Lecture: 22.10.2024, 29.10.2024, 05.11.2024, 08.11.2024, 19.11.2024, 22.11.2024, 26.11.2024, 29.11.2024, 03.12.2024, 10.12.2024, 13.12.2024, 17.12.2024,
07.01.2025, 10.01.2025, 14.01.2025, 21.01.2025, 24.01.2025, 28.01.2025, 04.02.2025, 07.02.2025, 11.02.2025, 14.02.2025
Problem class: 25.10.2024, 12.11.2024, 15.11.2024, 06.12.2024, 20.12.2024, 17.01.2025, 31.01.2025
We investigate both incompressible models (e.g., describing the motion of water) and compressible models (e.g., describing the motion of gases). By the end of the lecture, the audience will understand the distinct characteristics of these two types of models. Topics include the existence and uniqueness of weak and strong solutions, as well as the free boundary problem (if time permits).
The basic mathematical theory aligns with the lecture given in the summer semester of 2023, and we will also include compressible models in the winter semester of 2024/2025. Prerequisites: Analysis 1-3, Functional Analysis
Lecture notes (to be updated after each lecture)
Version 04.12.2024
Exercise sheets
Exercise sheet 1 (To be discussed on 25.10.2024)
Exercise sheet 2 (To be discussed on 12.11.2024)
Exercise sheet 3 (To be discussed on 15.11.2024)
Exercise sheet 4 (To be discussed on 06.12.2024)
Examination
Oral exam: Tuesday 18.02.2025.